ha (lvh262) – Homework 15.2 – karakurt – (56295) 1This print-out should have 20 questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.001 10.0 pointsFind the value of the integralI =Z10f (x, y) dxwhenf(x, y) = 6x + 5x2y .1. I = 3 +53y2. I = 3 −53y23. I = 6y + 5y24. I = 3 −53y5. I = 6y +52y26. I = 3 + 5y002 10.0 pointsDetermine the value of the double integralI =Z ZAf(x, y) dxdywhen f(x, y) = 3 andA =n(x, y) : 4 ≤ x ≤ 6, 3 ≤ y ≤ 6o.1. I = 202. I = 183. I = 194. I = 175. I = 16003 10.0 pointsDetermine the value of the iterated integralI =Z40Z21(1 + 2xy) dx dy .1. I = 242. I = 263. I = 304. I = 285. I = 32004 10.0 pointsEvaluate t he double integralI =Z ZA(3x − y) dxdywhenA =n(x, y) : 0 ≤ x ≤ 2, 0 ≤ y ≤ 1o.1. I = 82. I = 93. I = 74. I = 55. I = 6005 10.0 pointsEvaluate t he iterated integralI =Z41Z302(x + y)2dx dy .ha (lvh262) – Homework 15.2 – karakurt – (56295) 21. I = ln432. I =12ln433. I = 2 ln1674. I = ln1675. I =12ln1676. I = 2 ln43006 10.0 pointsEvaluate the double integralI =Z32Z20ex−ydxdy .1. I = e−3− e−2− e−1+ 12. I = e−3+ e−2− e−1+ 13. I = e−3− e−2+ e−1+ 14. I = e−3− e−2− e−1− 1007 10.0 pointsEvaluate the iterated integralI =Zln(6)0 Zln(5)0e2x−ydx!dy .1. I = 82. I = 103. I = 114. I = 95. I = 7008 10.0 pointsDetermine the value, I, of the integral ofthe functionf(x, y) =2x + y1 + 8y + y2over the rectangleA =n(x, y) : 1 ≤ x ≤ 3, 0 ≤ y ≤ 2o.1. I = ln 192. I = 2 ln 213. I = ln 214. I = 2 ln 195. I = 196. I = 21009 10.0 pointsEvaluate t he double integralI =Z ZA2 + x21 + y2dxdywhenA =n(x, y) : 0 ≤ x ≤ 2, 0 ≤ y ≤ 1o.1. I =53π2. I =116π3. I = 2π4. I =136πha (lvh262) – Homework 15.2 – karakurt – (56295) 35. I =73π010 10.0 pointsCalculate the value of the double integralI =Z ZA2x cos(x + y) d x dywhen A is the rectanglen(x, y) : 0 ≤ x ≤π2, 0 ≤ y ≤π2o.1. I = (4 − π)2. I = π3. I = −2(4 − π)4. I = −(4 − π)5. I = −2π6. I = 2π011 10.0 pointsEvaluate the integralI =Z ZA3xexydxdyover the rectangleA = { (x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 3 }.1. I = e3− 22. I =12e3− 33. I =12e3− 44. I =12e3− 25. I = e3− 36. I = e3− 4012 10.0 pointsEvaluate t he double integralI =Z ZA6xyeydxdywhenA =n(x, y) : 0 ≤ x ≤ 4, 0 ≤ y ≤ 1o.1. I = 482. I = 473. I = 514. I = 505. I = 49013 10.0 pointsFind the volume of the solid lying under theplanez = 9 − 3x − yand above the rectangleA =n(x, y) : 1 ≤ x ≤ 2 , 0 ≤ y ≤ 2o.1. volume = 5 cu. units2. volume = 8 cu. units3. volume = 9 cu. units4. volume = 7 cu. units5. volume = 6 cu. units014 10.0 pointsha (lvh262) – Homework 15.2 – karakurt – (56295) 4Find the volume of the solid l ying under thecircular paraboloid z = x2+ y2and above therectangle R = [−6, 6] × [−2, 2].1. 6402. 5123. 7684. 4805. 960015 10.0 pointsFind the volume of the solid bo unded bythe surfacez = 1 + (x − 2)2+ 5ythe planes x = 4 and y = 1 as well as thecoordinate planes.1. volume = 32. volume = 13. volume = 54. volume = 25. volume = 4016 10.0 pointsFind the volume of the solid in the first octantbounded by the cylinder z = 4 − y2and theplane x = 3.1. 182. 133. 124. 165. 20017 10.0 pointsFind the volume of the solid bounded bythe surfacez = 5 − xyand t he planesx = −4, x = 4, y = 0, y = 1,as well as the plane z = 0.1. volume = 52. volume = 13. volume = 24. volume = 45. volume = 3018 10.0 pointsEvaluate t he iterated integralI =Z30Z10x − y(x + y)3dy dx .1. I =342. I =543. I = 14. I =125. I =32019 10.0 pointsha (lvh262) – Homework 15.2 – karakurt – (56295) 5The sol id shown inlies bel ow the graph ofz = f (x, y) = 4 + x2− y2above the rectangle−1 ≤ x ≤ 1 , −2 ≤ y ≤ 2in the xy-plane. Determine the volume of thissolid.1. Volume = 23 cu. units2. Volume = 22 cu. units3. Volume = 25 cu. units4. Volume = 26 cu. units5. Volume = 24 cu. units020 10.0 pointsThe sol id shown inlies bel ow the graph ofz = f (x, y) = 4 + x2− y2and above the rectangle0 ≤ x ≤ 1 , 0 ≤ y ≤ 2in the xy-plane. Determine the volume of thissolid.1. volume =173cu. units2. volume =193cu. units3. volume = 5 cu. units4. volume =163cu. units5. volume = 6 cu.
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